Subtraction and overflow in two's complement

5 minAS Level1.1.3

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can subtract binary integers using two's complement, add negative numbers, and tell when a signed result has overflowed.

Subtracting is adding a negative

$A - B$ is the same as $A + (-B)$ . In two's complement that turns every subtraction into an addition, so the processor needs only one adder circuit.

Write $B$ in binary, then find its two's complement (invert, add 1). That's $-B$ .
Add it to $A$ using the normal rules.
Discard any carry out of the MSB. Keep the 8 bits that are left.

Worked example: 83 − 29

Calculate 0101 0011 − 0001 1101 (83 − 29) in 8-bit two's complement.

Have a go first?

Quick check

Fill in the blanksQuestion 1 · Apply

Calculate 0110 0100 − 0010 1000 (100 − 40) using 8-bit two's complement. The two's complement of 0010 1000 is . The 8-bit result, after discarding any carry, is .

Multiple choiceQuestion 2 · Recall

You subtract two 8-bit two's complement numbers by adding the two's complement, and a ninth bit carries out of the MSB. What should you do with it?

ADiscard it; the remaining 8 bits are the answer.BKeep it as the new MSB, making a 9-bit answer.CIt always means overflow, so the answer is invalid.DAdd it back on to the least significant bit.

Answer the 2 questions above to continue.

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